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Simplifying b2 + -8b + -60 = 0 Reorder the terms: -60 + -8b + b2 = 0 Solving -60 + -8b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -8b + 60 + b2 = 0 + 60 Reorder the terms: -60 + 60 + -8b + b2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -8b + b2 = 0 + 60 -8b + b2 = 0 + 60 Combine like terms: 0 + 60 = 60 -8b + b2 = 60 The b term is -8b. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8b + 16 + b2 = 60 + 16 Reorder the terms: 16 + -8b + b2 = 60 + 16 Combine like terms: 60 + 16 = 76 16 + -8b + b2 = 76 Factor a perfect square on the left side: (b + -4)(b + -4) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (b + -4) equal to 8.717797887 and -8.717797887.Subproblem 1
b + -4 = 8.717797887 Simplifying b + -4 = 8.717797887 Reorder the terms: -4 + b = 8.717797887 Solving -4 + b = 8.717797887 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = 8.717797887 + 4 Combine like terms: -4 + 4 = 0 0 + b = 8.717797887 + 4 b = 8.717797887 + 4 Combine like terms: 8.717797887 + 4 = 12.717797887 b = 12.717797887 Simplifying b = 12.717797887Subproblem 2
b + -4 = -8.717797887 Simplifying b + -4 = -8.717797887 Reorder the terms: -4 + b = -8.717797887 Solving -4 + b = -8.717797887 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = -8.717797887 + 4 Combine like terms: -4 + 4 = 0 0 + b = -8.717797887 + 4 b = -8.717797887 + 4 Combine like terms: -8.717797887 + 4 = -4.717797887 b = -4.717797887 Simplifying b = -4.717797887Solution
The solution to the problem is based on the solutions from the subproblems. b = {12.717797887, -4.717797887}
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